Applications of Functional Analysis and Operator Theory: Volume 200

ISBN-13: 9780444517906 / Angielski / Twarda / 2005 / 432 str.

V. Hutson; J. Pym; M. Cloud

Opis

Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces.

Key Features

- Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering.
- Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results.
- Introduces each new topic with a clear, concise explanation.
- Includes numerous examples linking fundamental principles with applications.
- Solidifies the reader's understanding with numerous end-of-chapter problems.

-Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering.
-Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results.
-Introduces each new topic with a clear, concise explanation.
-Includes numerous examples linking fundamental principles with applications.
-Solidifies the reader's understanding with numerous end-of-chapter problems.

Spis treści

1. Banach Spaces2. Lebesgue Integration and the Lp Spaces3. Foundations of Linear Operator Theory4. Introduction to Nonlinear Operators5. Compact Sets in Banach Spaces6. The Adjoint Operator7. Linear Compact Operators8. Nonlinear Compact Operators and Monotonicity9. The Spectral Theorem10. Generalized Eigenfunction Expansions Associated with Ordinary Differential Equations11. Linear Elliptic Partial Differential Equations12. The Finite Element Method13. Introduction to Degree Theory14. Bifurcation Theory